Proceedings of SALT 25: 576-594, 2015
The morphosemantics of Spanish indefinites* Luisa Martí Queen Mary University of London
Abstract I analyze the Spanish indefinites algún and algunos as a paucal and a greater paucal determiner, respectively, contrary to the common assumption that views the former as singular and the latter as plural. I use Harbour’s (2014) feature [±additive], and the possibility of repeating that feature, in order to do so. I propose a transparent word-internal compositional analysis of the two determiners, where alg- contributes [−additive] to both of them. I discuss consequences for the semantics of morphological plurality in nouns and for the analysis of ignorance implicatures.
Keywords: determiners, number, paucals, plurals, ignorance 1 Introduction Previous work on Spanish indefinite determiners has focused on scope (AlonsoOvalle and Menéndez-Benito (AO&MB) 2013; Martí 2007), ignorance effects (AO&MB 2010, 2011), contrasts between unos and algunos (Gutiérrez-Rexach 2001; Martí 2008), or unos and its group semantics (López Palma 2007). However, no previous discussion has elucidated the differences in number import between algún and algunos, which this paper sets out to do. The basic facts are as follows (cf. AO&MB 2010, 2011; Martí 2008):1, 2 (1)
Hay alguna mosca en la sopa. there.is ALGÚN.FEM fly in the soup ‘There is one or a very small number of flies in my soup.’
(2)
Hay algunas moscas en la sopa. there.are ALGUNOS.FEM flies in the soup ‘There are several flies in my soup.’ (more flies than in (1))
*
Thanks to Klaus Abels, Donka Farkas, Daniel Harbour and audiences at University of Illinois at Urbana-Champaign, Queen Mary University of London and SALT25 in Stanford for inspiration, comments, and questions, as well as the support of a British Academy/Leverhulme Trust Small Research Grant (2013-2015) during the research that led to this paper. 1 Translations are approximate throughout. 2 FEM = feminine. © 2015 Martí
Morphosemantics of Spanish indefinites
Example (1) is true when there are one or a very small number of flies in the soup, where the upper boundary of this quantity is imprecise. In (2), on the other hand, there are more flies than in (1). Again, the upper boundary of this quantity is imprecise. If there were just two, perhaps three, flies in my soup, algún would be appropriate, but algunos wouldn’t. If there were six or seven flies, algunos would be appropriate, but algún wouldn’t. I argue that the approximative number distinctions that some languages of the world make in their (pro)nominal domain, namely, between paucal and greater paucal, are actually observed in the Spanish data. I propose that plural morphology in algunos contributes the semantics of Harbour’s (2014) [+additive] feature, and that alg- contributes [−additive] in both algún and algunos. I claim that all that the analysis requires is to import into the DP domain part of the technology already introduced by Harbour for number in the NP domain. The remainder of the paper is organized as follows. I discuss the data in more detail in Section 2. In Section 3 I introduce Harbour’s theory of number, and then my proposal. Some of the evidence that justifies it is in Section 4. In Section 5 I discuss a number of consequences of the analysis. Ignorance implicatures associated with algún but not with algunos are discussed in Section 6. Section 7 is the conclusion. 2 Data Examples (3) and (4) show that algún is compatible with a non-singular interpretation (from AO&MB 2010): (3)
Mi coche tiene alguna abolladura. my car has ALGÚN.FEM dent ‘My car has one or a very small number of dents.’
(4)
Juanito todavía tiene algún diente de leche. Juanito still has ALGÚN tooth of milk ‘Juanito still has one or a very small number of baby teeth.’
According to AO&MB (2010: 24) “[(3)] says that the speaker’s car has some unspecified number of dents, and [(4)] indicates that Juanito has some baby teeth, but the speaker is not sure how many”. That is, my car could have a (very small) number of dents, and Juanito could still have a (very small) number of baby teeth (one dent and one tooth are also possible). That the speaker expresses ignorance with respect to the number of dents and baby teeth is an additional aspect of the meaning of algún, but not of algunos, which I discuss in Section 6. Likewise, according to (5), based on Zamparelli (2007), Juan weighs a few more kilos than he should (or possibly just one):
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Martí
(5)
Juan pesa algún kilo de más. Juan weighs ALGÚN kilo of more ‘Juan weighs one or a very few more kilos than he should.’
The naturally occurring (6) and (7) clearly indicate the possibility of a nonsingular reading for algún; (7) is particularly revealing because los perros (underlined) ‘the dogs’ is used in a subsequent sentence to refer back to algún perro: (6)
La presencia de alguna mosca blanca no es importante, sólo cuando se trate de grandes colonias debería considerarse un problema. ‘The presence of one or a very small number of whiteflies is not important, it is only when there are big groups that a problem arises.’ (http://www.ecoagricultor.com/tratamientos-ecologicos-pulgon-moscablanca-arana-cochinilla, retrieved on 9/7/2015)
(7)
Dos o tres veces el lejano ladrido de algún perro nos dio algo de esperanza, pero la noche cerrada no mostraba nada y los perros se callaban o estaban en otra dirección. ‘Two or three times the distant bark of one or a very small number of dogs gave us some hope, but the night was dark and didn’t allow us to see anything and the dogs would stop barking or they were in a different direction.’ (E. Che Guevara & A. Granados, Viaje por Sudamérica, 1992)
That algunos is not just plural is illustrated in (8), where it contrasts with “two”: (8)
Boss: Hay algunas moscas en there.are ALGUNOS flies in ‘There are several flies in my soup.’ Waiter: No, sólo hay dos/#cinco. No only there.are two/five ‘No, there are only two/#five.’
la the
sopa. (=(2)) soup
If algunos was semantically plural, the exchange in (8) with dos ‘two’ wouldn’t be felicitous, because two is a plurality. It’d be just as infelicitous as it is when algunas moscas is replaced by the bare plural moscas (which, I claim later, is indeed semantically plural). With cinco ‘five’, the algunos exchange is infelicitous because there is no incompatibility between five and several. In (9), it is possible to specify how many books one bought at the fair, but not if the number of books is less than three (or four, for some speakers):3 3
AO&MB (2011) discuss examples that seem incompatible with (8) and (9), such as (i):
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Morphosemantics of Spanish indefinites
(9)
Me compré algunos libros en la feria. myself bought ALGUNOS books in the fair En concreto, #uno/#dos/?tres/cuatro/cinco/seis/siete/ocho in concrete one/two/three/four/five/six/seven/eight ‘I bought myself several books at the fair. More specifically, #one/#two/?three/four/five/six/seven/eight.’
3 Paucity In this section I first introduce the basics of Harbour’s system (Section 3.1). I then use his feature [±additive] to account for the number distinction observed above between algún and algunos (Section 3.2). 3.1
Paucity in nouns
Natural languages make use of number categories that are encoded on pronouns or nouns, including singular, dual, trial, minimal, augmented, unit augmented, paucal, greater paucal, greater plural, global plural, or plural (see Corbett 2000 and Harbour 2014 for definitions and illustrations). Paucal and greater paucal occur in the pronoun system of, for example, Sursurunga, an Oceanic language of New Ireland (Corbett 2000: 26-30; Hutchinsson 1986). In addition to singular, dual and plural personal pronouns, this language distinguishes between instances where the referent of the pronoun is constituted by just a small number of individuals ((lesser) paucal) vs. instances where that referent comprises a few more individuals than that (greater paucal). There are number systems that express no number distinctions at all (Pirahã), those that express what Sursurunga does, those that express singular, dual, trial, paucal and plural (Marshallese), and others. There are also a number of possibilities that are never attested. E.g., there are no languages that distinguish only singular, dual and paucal, or only paucal and plural. Indeed, there are Greenberg-style typological generalizations in this area: there is no trial without dual, no greater paucal without (lesser) paucal, no dual without singular, etc. See Harbour (2014) for more details. (i)
María vive con algunos estudiantes, en concreto, María lives with ALGUNOS students in concrete con Pedro y con Juan. with Pedro and with ‘María lives with several students, more precisely, with Pedro and with Juan.’
(i) is odd for me and the speakers I’ve consulted—algunos requires a number greater than two. Given that algunos expresses an imprecise number, however, some data disagreement is predicted.
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Martí Paucity, abundance, and the theory of number Harbour’s account of this typology rests on the following195 assumptions: (a) the 0 syntax of NP is as in (10); (b) n structures roots into join-semilattices (cf. Link (9) λP λx (Q(x) ∧ ∀y (Q( y) → Q(x ! y)) ∧ Q " P) 1983); threeofsemantic features can appearofinP.)Num0: [±additive], [±atomic], (The set of (c) elements a join-complete proper subregion [±minimal]; these features oneverything the lattices by nP; (e) a Q is a contextually supplied (d) free variable, and Q " Poperate means that in Q isprovided in P parameter regulates whether the repetition of a particular feature in Num0 is but not vice versa: ∀z(Q(z) → P(z)) ∧ ¬∀z(P(z) → Q(z)). allowed; (f) the asemantic range of denied the cut [±additive] Finally, given that weand are defining property that can be (asof well as asserted),is subject to social convention. only the correct parts should fall within the scope of negation. The negation should
characterize points that are within the join-incomplete subregion of P. It should not characterize (10) points that, say, are notNP in the lattice at all (the cat-dog problem). That is, Q(x) and Q " P must beqp beyond the scope of negation, since they force x to be within NumP both Q and P. Hence, we treat the predication of Q and the inclusion of Q in P as preqp suppositions. Num0 nP (10) [±additive] = λP λx (¬)∀y (Q( y) → Q(xqp ! y)) presuppositions: Q(x), Q " P n0 √ (The set of elements of join-(in)complete subregion P.) Together, assumptions result in different meaning with respect The parenthetic negation these signifies that ¬ is present for the minus value, absent fordistinctions plus. If featuresto could speak, this one would say: me a lattice region, I’ll giveof attested number (pro)nominal number in a‘Give language and in the and typology you back thesystems set of points that languages comprise a subregion of thatLet region’. Askhow whatpaucals is so spe-and greater paucals in the of the world. us see cial about that the feature would respond: ‘Assert me and the subregion will be areand derived in this system. join-complete: add any point of the subregion to any otherthere and you’ll stillcrossing be in the subConsider the simplified (because are no lines) view of a joinregion. Deny me, and the subregion will be join-incomplete: sometimes adding points semilattice in (11) (images from Harbour 2014); the atomic layer is at the bottom: will keep you in the subregion, sometimes it won’t’.
(11) P Q+
P Q–
❅ ❅
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Figure 5. A bounded region, Q–, and an unbounded top, Q+.
P designates the lattice. The subsection indicated as Q+ (with the black dots) is the 4, 5 semanticsuggests, contribution of [+additive], in (12): As this paraphrase (+additive) defines a different region from (−additive).
For the latter, the Q that 10 introduces is a bounded region; for the former, Q is an unbounded region. Figure 5 illustrates a plural Q and a paucal Q, for a given P, arising from (+additive(P)) and (−additive(P)), respectively. thatsays these areQdiffer4 Q is a free variable, ‘x⊔y’ is the join ofTox emphasize and y, ‘Q⊏P’ that is a proper subpart of P. cf. ent Qs, they Krifka’s are labeled according to the feature that defines them, as Q and Q−.7 It is + (1989, 1992) notion of cumulativity. 7
5
(12) and (13) are modified versions of Harbour’s proposal. Harbour expresses the relation of Q
This is different from more familiar number features: (+atomic) picks out the atoms of a lattice, and a presupposition. thinkout (12) are ofpreferable and and the(−minimodifications don’t seem to (−atomic) picksto outPitsascomplement; (+minimal)I picks the and lowest(13) stratum a lattice region, have major consequence for his account. Of course, Sauerland (2003) has proposed a mal) picks out its complement. Figure 5 represents choices for Q+ and Q− for which this complement relation account holds, but other presuppositional values could have been chosen.of number. While a full comparison between Sauerland’s proposal and My diagrams of paucals also portray a specific upper bound for the paucal, a reflection of my limited drawing skills. In practice, two sources for approximative numbers’ approximativeness are imaginable, vagueness versus variability. They might be inherently vague as to their cut-off point;580 or, within any model, they might have a specific cut-off point, but with that specific point varying from model to model. See Chierchia 2010 for in-depth discussion of vagueness and nouns.
Morphosemantics of Spanish indefinites
(12)
[[+additive]] = λPλx. Q(x) & Q⊏P & ∀y (Q(y)→Q(x⊔y))
The feature [+additive] takes a set of individuals and returns a proper subset of it. Each member of this proper subset is such that, when joined with any other member of the subset, results in a member of the subset (this characteristic is called join-completeness). [+additive] returns a subsection of the lattice that is join-complete. Where the cut for [+additive] (i.e., the horizontal line in (11)) occurs can vary and is subject to social convention. The feature [−additive] also takes a set of individuals and returns a proper subset of it. Which subset that is is determined as follows: for not all members of this proper subset is it the case that, when joined with some other members of the subset, the result is a member of the subset. [−additive] returns a subsection of the lattice that is join-incomplete (Q_ in (11)): (13)
[[−additive]] = λPλx. Q(x) & Q⊏P & ¬∀y (Q(y)→Q(x⊔y))
[−additive] with a low cutting point results in a paucal meaning. How many individuals actually count as paucal in a given language is subject to social convention. It could be that all those plural individuals formed of one, two, three or four atoms do, or that those formed of two, three, four or five atoms do, etc. Examples discussed in Harbour include Koasati (Muskogean, USA), where the nouns that take a paucal suffix do so for more than 2 but less than 5 or 6 N; Yimas (Ramu-Lower Sepik, Papua New Guinea), where it is from 3 up to about 7 N, variable depending on contexts; and Boumaa Fijian (Austronesian, Fiji), where the paucal means ‘proportionately few’.6 For greater paucals, recall that a parameter makes it possible to repeat a feature in Num0. Not all combinations of values for a feature yield satisfiable results, however. The combination [+additive (−additive (P))], e.g., is unsatisfiable because it is not possible to find a join-complete region within a join-incomplete one. The combination [−additive (+additive (P))] is, and gives rise to a greater paucal meaning when the cut off point is low. We first obtain a join-complete subregion of a lattice, Q+, and next we obtain a join-incomplete subregion of Q+, Q’ (image from Harbour 2014):7
mine cannot be undertaken here, notice that in Harbour’s proposal the contribution of number is an entailment; what is presupposed is just ‘Q(x) & Q⊏P’. 6 There are further constraints on the resulting semilattices (Harbour 2014: 196-7, 210-2). 7 [+additive (+additive (P))] and [−additive (−additive (P))] are satisfiable but violate other constraints (Harbour 2014: 204-5). For more on [+additive (+additive (P))], see Section 5.
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Thinking informally, one quickly sees that (+additive(−additive(P))) is unsatisfiable. It takes a join-incomplete part of P and ‘looks for’ the join-complete proper subregion within it (see online Appendix B). The alternative formula, (−additive(+additive(P))), by contrast, is satisfiable. After P is divided into join-incomplete and join-complete subregions, (−additive) divides the join-complete subregion, (+additive(P)), into join-incomplete and join-complete subsubregions. There are consequently two bounded regions, one stacked on top of the other. Figure 7 represents these as partitions. Q− is the nonadditive subregion arising from (−additive(P)) and Q+ the unbounded region from (+additive(P)). Q+ is split into a second join-incomplete subregion, Q′, by (−additive(+additive(P))), and this induces a new, smaller, join-complete complement region, Q+\Q′ (that is, Q+ minus the subregion Q′).12
(14)
P
Q+
Q+\Q′
P
Q+
Q′
P
Q–
Martí
❅ " ❅ " ❅ " " ❅ " ❅ " ❅ " ❅ ❅ " ❅ " ❅ " ❅ " ❅ ✇" " ❅" ✇ ✇ ✇ ✇ " ❅ ❅ ❅✇ " " ❅ " ❅ "❅ " ❅ "❅ " ❅ " ❅ " ❅ ❅ " ❅ ✇" ❅ ✇" ❅ ✇" " ❅ " ❅ ✇ ✇ " ❅ " ❅ ❅ ❅ " " "❅ " ❅ ❅ " " ❅ ❅ " ❅ " ❅ " " ❅ ❅ " " ❅✇ ❅ ✇" ❅✇ ❅" " " ✇ ❅✇ " ❅✇ "❅ ❅ "❅ "❅ " "❅ " ❅ " ❅ ❅ " ❅ " " ❅ ❅ ✇" " ❅ ✇ ✇ ✇ ✇ " ❅ ❅ ❅ ❅" " " " ❅ "❅ " ❅ " ❅ "❅ ❅ " " ❅ ❅ " ❅ ✇" ❅ ✇ ❅ ✇" ❅ ✇" " ❅ ✇" ✇ " ❅ ❅ ❅ " ❅ " ❅ " " " ❅ " ❅ " ❅ " ❅ " ❅ " ❅ " ❅ " ❅ ❅" ❅✇ " ❅✇ " ❅✇ " " ✇ ❅✇ "❅ "❅ "❅ "❅ "❅ ❅ " ❅ ❅ " ❅ " ❅ " ❅ " " " ❅ ✇ ✇ ✇ ✇ ✇ ✇ ❅ ❅" ❅" ❅" ❅" " " ❅ "❅ "❅ "❅ "❅ " ❅ " ❅ ❅ " ❅ " ❅ " ❅ " ❅ " " ❅ ✇ ✇ ✇ ✇ ✇ ❅ " ❅ " ❅ " ❅ " ❅ " ❅ ❅ " ❅ " ❅ " ❅ " ❅ " ❅ " ❅❣ " ❅❣ " ❅❣ " ❅❣ " ❅❣ " ❅❣ " " ❅ " ❅ " ❅ " ❅ ❅❣ " ❅ ❅ " ❅ " ❅ " ❅ " ❅❣ " ❅❣ " " ❅ " ❅ " ❅ " ❅ " ❅❣ " ❅ ❅ " ❅ " ❅ " ❅ " ❅❣ " ❅❣ " "
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If a language exploits this option, it will have two approximative numbers. If the cut is low for both, then we have a language like Sursurunga, with a (lesser) and a greater paucal. If the first cut is low and the second high, we have a 12 The paucal smaller join-complete region cannot be defined by (−additive(−additive(P))), as [−additive −additive … ] language falls foul of the axiom (§5.1). withofaextension paucal and a greater plural, such as Mele-Fila (Austronesian, Vanuatu). Both cuts can be high, as in Warekena (Arawakan, Brazil/Venezuela), which distinguishes plurals from greater plurals from plurals of abundance. Figure 7. A lesser bounded region, Q–, greater bounded region, Q′, and an unbounded top, Q+\Q′. Note: the portion of a number system illustrated is paucal (Q−), greater paucal (Q′), and plural (Q+\Q′). Higher placement of one or both cuts is possible, as discussed below.
3.2
Paucity in determiners
My proposal for the internal structure of algún and algunos is as follows:8 (15) DP wo -un wo algwo (-s) NP Alg- contributes [−additive] with a vague and low cut: (16)
[[alg-]] = [[−additive]] = λPλx. Q(x) & Q⊏P & ¬∀y (Q(y)→Q(x⊔y))
I assume that -un is a generalized existential quantifier and has, as desired, the same semantics as the indefinite un: (17)
[[-un]] = λR.λS.∃z R(z) & S(z)
Morphologically singular nouns, such as mosca ‘fly’, are semantically numberneutral and thus their denotation contains both atomic and plural individuals. Putting these pieces together in the order indicated in (15), we have: 8
The morpheme -o-/-a- (alguna, algunos, algunas) marks gender agreement. It plays no role here.
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Morphosemantics of Spanish indefinites
(18)
[[alg-]] ([[mosca]]) = λx. Q(x) & Q⊏[[mosca]] & ¬∀y (Q(y)→Q(x⊔y))
(19)
[[-un]] ([[alg-]] ([[mosca]])) = λS.∃z Q(z) & Q⊏[[mosca]] & ¬∀y (Q(y)→Q(z⊔y)) & S(z)
For (1), repeated here, this results, correctly, in the vague, approximative semantics of the paucal, in (21) (recall Q_ in (11)): (20)
Hay alguna mosca en la there.is ALGÚN.FEM fly in the ‘There is one or a very few flies in my soup.’
sopa. (=(1)) soup
(21)
[[Hay alguna mosca en la sopa]] = ∃z Q(z) & Q⊏[[mosca]] & ¬∀y (Q(y)→Q(z⊔y)) & [[en_la_sopa]](z)
Notice that we ensure that atoms are included in the semantics of algún because of the complement completeness constraint (Harbour 2014: 197), which says that the complement of Q_ must be join-complete: (22)
P is join-complete iff ∀x,y (P(x) & P(y) → P(x⊔y)) (i.e., the sum of any two elements of P is in P)
That is, I assume the complement of any Q_ is a possible value for Q+. If atoms were excluded, the complement of Q_ would not be join-complete. Complement completeness also excludes other unwanted cuts (see Harbour 2014). I assume that the -s of algunos, as well as the -s of morphologically plural nouns, contributes [+additive]: (23)
[[-salgunos]] = [[-snoun]] = [[+additive]] = λPλx. Q(x) & Q⊏P & ∀y (Q(y)→Q(x⊔y))
(24)
[[moscas]] = [[+additive]]([[mosca]]) = λx. Q(x) & Q⊏[[mosca]] & ∀y (Q(y)→Q(x⊔y))
I also assume that the cut for [+additive] when it appears within NP (N[+additive]) is the lowest cut that satisfies it; i.e., it removes just the atomic layer. I assume that the cut for [+additive] when it appears with D (D-[+additive]) is vague and low. Crucially, the meaning for alg- in algunos is still [−additive], and the meaning of -un- is still as before, as the null hypothesis dictates, given that alg- and -un- are part of both algún and algunos. Continuing up the tree, we have: (25)
[[-salgunos]] ([[moscas]]) = [[+additive]] ([[moscas]]) = λx. Q(x) & Q⊏[[moscas]] & ∀y (Q(y)→Q(x⊔y))
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(26)
[[alg-]]([[-salgunos]]([[moscas]])) = [[−additive]]([[-salgunos]]([[moscas]])) = λx. Q(x) & Q⊏{x: R(x) & R⊏[[moscas]] & ∀v (R(v)→R(x⊔v))} & ¬∀y (Q(y)→Q(x⊔y))
(27)
[[-un-]] ([[alg-]]([[-salgunos]]([[moscas]]))) = λS.∃z Q(z) & Q⊏{x: R(x) & R⊏[[moscas]] & ∀v (R(v)→R(x⊔v))} & ¬∀y (Q(y)→Q(z⊔y))] & S(z)
(26) is a set of individuals. It contains all of those individuals for which the following is true: they are part of a join-incomplete proper subsection of a joincomplete subsection of the lattice obtained by the cut introduced by D-[+additive] (recall Q’ in (14)). This, in turn, is a proper subsection of the lattice obtained by the cut introduced by N-[+additive]. (27) says that, given a VP, there is an individual in that join-incomplete subsection of the lattice that VPs. This results, correctly, in a greater paucal meaning for (2) (repeated) in (29): (28)
Hay algunas moscas en there.are ALGUNOS.FEM flies in ‘There are several flies in my soup.’
la the
sopa. (=(2)) soup
(29)
[[hay algunas moscas en la sopa]] = = ∃z Q(z) & Q⊏{x: R(x) & R⊏[[moscas]] & ∀v (R(v)→R(x⊔v))} & ¬∀y (Q(y)→Q(z⊔y))] & [[en_la_sopa]](z)
Thus, algún and algunos are paucals because they both contain alg-. Algún is a lesser paucal because of alg-. Algunos is a greater paucal because it adds -s to alg. Un (and unos; see below) is not a paucal because it doesn’t contain alg-. And both algún and algunos are existential quantifiers because they both contain -un-. What the proposal assumes in order to achieve these results is the following: (a) alg- is [−additive] (with an imprecise and low cut); (b) -un- is an existential generalized quantifier; (c) -salgunos is [+additive] (with an imprecise and low cut); (d) -snoun is [+additive] (with the most minimal cut that satisfies it); (e) morphologically singular nouns are semantically number-neutral. Assumption (a) is at the core of my proposal and assumption (b) is the null hypothesis. Evidence for (c) and (d) is provided in Section 4. Assumptions (d) and (e) are further discussed in Section 5.9
9
This account of both algún and algunos needs to be supplemented with an account of their notmany/all implicature, probably in the terms of a classical scalar implicature. On implicatures, see Section 6.
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4 Evidence for [+additive] in nouns and in algunos Regarding (c) above, evidence that the semantic contribution of -salgunos is [+additive] comes from the consideration of pluralia tantum nouns such as gafas ‘glasses’, that is, of nouns which are formally, but not semantically, plural. Algunas gafas, where algunos is combined with such a noun, entails the existence of several pairs of glasses. [+additive] cannot come from gafas, for pluralia tantum nouns are not semantically plural. Evidence that gafas is, in fact, semantically singular, comes from its combination with other indefinites, like unos: importantly, unas gafas, as López Palma (2007: 253) notes, entails the existence of just one pair of glasses.10 Thus, semantic plurality can only come from algunos. If [+additive] is a crucial ingredient of greater paucality, if alg- is not [+additive] (this would give the wrong semantics for algún), and if -un- is not [+additive], then -salgunos must be [+additive]. Because *alguna gafas is impossible, we further conclude that -salgunos is also a number agreement marker. Thus, we have here a complex relationship between form and meaning in the case of -s: it contributes [+additive] in the case of algunos (and in the case of regular nouns, i.e., nouns that are not pluralia tantum; see below); in addition, it is a marker of number agreement in algunos (and unos; see footnote 10). Let us reason our way to assumption (d), namely, that morphologically plural nouns are [+additive] (or, equivalently in my proposal, semantically plural). Recall, first, that algún NP VP is compatible with there being just one NP VP, so we need atomic individuals in the denotation of mosca ‘fly’. Because algún is also compatible with there being more than one fly, we need non-atomic individuals too. If these are contributed directly by the NP, alg- can simply be [−additive] and the account of its paucality is straightforwardly imported from Harbour, as in Section 3.2. For this account of algún to work, then, the denotation of nouns like mosca (i.e., count nouns that are morphologically unmarked for number) must contain both plural and singular individuals. This, in turn, makes it natural to assume that nouns like moscas (i.e., count nouns that are morphologically marked for number) denote sets of plural individuals. That is, that [[-sregular-noun]] is the same as [[-salgunos]], i.e., [+additive] (with a difference in where the cut is). But there is, in fact, evidence that this must be the case: because unas moscas is plural (i.e., unas moscas entails the existence of a plurality of flies), and unos is not (since unas gafas is not), the only source of plurality there is -sregular-noun.
10
What this means for the semantics of unos, and for -sunos in particular, is interesting too. My hypothesis is that -sunos is just a number agreement marker, with no semantics; cf. *una gafas.
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5 The interpretation of number morphology in nouns One important consequence of the above proposal, then, is that morphologically plural nouns are semantically additive/plural, and morphologically unmarked/singular nouns are semantically number-neutral. The issue of how exactly number semantics is mapped to number marking is a long-standing issue that is still controversial and requires further discussion. The place to begin discussing it is, I believe, Sauerland (2003), since a proposal about the semantics of both morphologically number-marked nouns and morphologically numbermarked determiners is made there. Sauerland (2003) proposes a general, presuppositional theory of number for the determiner-nominal domain and thus the proposal I make in this paper needs to be carefully contrasted with it. While, for reasons of space, this is a task that cannot be fully undertaken here, I would like to argue that my proposal seems better suited for the account of algún and algunos. One of the crucial assumptions in Sauerland’s theory is that there is only one syntactic location for the interpretation of number in this domain (ϕP, above every projection related to the noun and the determiner). It is here that features such as [Sg] and [Pl] are interpreted; everything in the determiner or nominal domains that “looks” plural (i.e., -s on nouns in English), is a mark of agreement with ϕ. While in principle it is possible to formulate the right semantics for paucal and greater paucal features in ϕ, a morphologically-transparent account of algún and algunos (i.e., one that tries to explain why alg- is part of both, and how -salgunos affects meaning) necessitates more than one location for the interpretation of number. Given the semantic plurality of unas moscas, the semantic singularity of unas gafas and the semantic plurality of algunas gafas, we need to say that a marker of plurality in the noun domain is interpreted there (since moscas is to blame for plurality in unas moscas), and that a marker of plurality in algunos is interpreted there (since algunos is to blame for plurality in algunas gafas). Importantly, if my account is right, alg-, and not just (some instances of) -s, spells out number-related meaning too—that’s a second locus of number semantics just for the D domain. My proposal follows Bennett (1974), Chierchia (1998), Farkas and de Swart (2010), Harbour (2014), among others, in the idea that the morphological plural feature is semantically interpreted as plural. On the other hand, Krifka (1989), Lasersohn (1998, 2011), Sauerland (2003), Sauerland et al. (2005), Spector (2007), and others, propose that that feature is not semantically plural (because it is not interpreted at all, or because morphologically marked plural nouns denote sets that contain both atomic and non-atomic individuals, or because they have a naïve semantics). A related question is what semantics the morphologically unmarked/singular is given.
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While, as Farkas and de Swart (2010) argue, an approach that treats the morphologically marked plural as making a semantic contribution captures better the fact that, cross-linguistically, languages with a singular/plural contrast morphologically mark the plural, not the singular, there are nevertheless wellknown problems with the proposal I am advocating here. For example, downward-entailing contexts, among others, are well known for raising problems (Farkas and de Swart 2010; Lasersohn 1988; Schwarzschild 1996 and others). Consider (30): (30)
No students came to the party.
This sentence is true only if there wasn’t a single student who came to the party, and false even if only one student came to the party. However, if morphologically plural nouns denote sets of plural individuals only, the truth-conditions of (30) come out wrong: the meaning of the sentence is not that there are no pluralities of students who came (this is true if one student came). There are a number of solutions to this problem, of different scope, including a different semantics for downward-entailing quantifiers (as in Chierchia 1998, though see Lasersohn 2011), or a pragmatic account as to why “inclusive” interpretations of the plural (i.e., where they allow atomic reference) are obligatory in these contexts, as in Farkas and de Swart 2010. My account entails that at least one of these solutions has to be right. Going back to my account for algunos, an additional consequence of my proposal is that algunas moscas is “doubly” additive: there is D-[+additive] and N-[+additive] in it. In relation to this, consider that Harbour (2014: 205) argues that the axiom of extension ({a, a} = {a}) bans combinations such as [+additive (+additive (P))]. I suggest that because the two instances of [+additive] in algunas moscas come from different sources (one from the noun, the other from the determiner), this constraint is not violated. This might be, indeed, the explanation for the fact that unos can be “pluralized” with cuantos (or, possibly, with pocos ‘few’, as in unos pocos), whereas algunos cannot, as illustrated in (31): (31)
unas gafas ‘one pair of glasses’ unas cuantas gafas ‘several pairs of glasses’ algunas gafas ‘several pairs of glasses’ *algunas cuantas gafas
We can explain (31) if -scuantos = [+additive], cuantos (or pocos) is part of the determiner domain and Harbour’s extensionality axiom applies within domains, not across domains. That is, the determiner domain of algunas cuantas gafas would contain [+additive (+additive (P))] within a single domain. That the -snoun of regular, non-pluralia-tantum nouns contributes [+additive] means it is possible that the plurality of Spanish regular nouns is solely the result
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of [+additive], not of [−atomic]. We could assume that -salgunos contributed [+additive] and that -snoun contributed [−atomic], but this is more costly than saying that -snoun and -salgunos are, semantically and morphologically, the same. Notice that the results of [+additive] and [−atomic] for nouns are indistinguishable if the cut for N-[+additive] is the lowest possible. Finally, in Martí 2008, I argued that both unos and algunos are semantically plural. The more complete set of facts considered here, however, leads to a revision of that claim. The decompositional spirit of the account provided there survives in the present account; note that a syntactic domain for the interpretation of determiner number was also hypothesized in that work. I leave a full-fledged consideration of all the facts discussed in the earlier work, however, for another occasion—they are partly independent of number semantics. It will also be necessary to consider López Palma’s (2007) results for unos in the future. 6 Ignorance Algún triggers ignorance implicatures11 about number and/or identity (AO&MB 2010). Algunos, on the other hand, does not (AO&MB 2011). In this section I demonstrate that AO&MB’s account of the ignorance implicature of algún cannot be maintained if algún has the paucal semantics argued for here. Their account of the lack of such implicatures with algunos, on the other hand, can (though see footnote 14). Consider (32): (32)
Pedro se compró algún libro en la feria. Pedro himself bought ALGÚN book in the fair ‘Pedro bought himself one or a very small number of books at the fair.’
By using algún in (32), the speaker signals that she does not know which book or books Pedro bought himself at the fair, or how many (though she does know it is one or a very small number). It is thus inappropriate for the hearer to ask back which or how many books he bought. As expected for an implicature, this ignorance component disappears in downward-entailing contexts. AO&MB (2010, 2011) propose that algún and algunos introduce a requirement such that their domain cannot be a singleton set. In their proposal, the meaning of algún is as in (33), where the anti-singleton requirement is modeled using a subset selection function ‘f’: (33)
[[algún (P)]] = λS: anti-singl(f).∃z (f(P))(z) & S(z)
The truth-conditions for a sentence like (32) are in (34), for books b1, b2 and b3:
11
And indifference implicatures, but I put indifference aside here. 588
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(34)
The speaker believes (BS) ∃z z∈f({b1, b2, b3}) & bought(z)(Pedro)
The possible assertions expressed by (34), depending on the choice of nonsingleton domain, are as follows: (35)
A1: BS ∃z z∈{b1, b2} & bought(z)(Pedro) A2: BS ∃z z∈{b1, b3} & bought(z)(Pedro) A3: BS ∃z z∈{b2, b3} & bought(z)(Pedro) A4: BS ∃z z∈{b1, b2, b3} & bought(z)(Pedro)
Thus, one possible assertion expressed by our sentence is that the speaker believes that Pedro bought b1 or b2 at the fair (A1). Following Kratzer and Shimoyama (2002), AO&MB propose that, upon hearing a sentence with algún, the hearer asks why the speaker chose an indefinite with an anti-singleton requirement, and concludes, Gricely, that she must have done so because choosing a singleton domain would not have been conducive to truth. We thus need to consider the singleton competitors to (34), listed in (36): (36)
C1: BS ∃z z∈{b1} & bought(z)(Pedro) C2: BS ∃z z∈{b2} & bought(z)(Pedro) C3: BS ∃z z∈{b3} & bought(z)(Pedro)
The hearer concludes that the speaker believes that there is a book that Pedro bought at the fair ((34)), and that it is not the case that any of the singletondomain competitors are true; i.e., the speaker does not believe that (i.e., does not know if) Pedro bought b1 (C1), and the speaker does not know if Pedro bought b2 (C2), and the speaker does not know if Pedro bought b3 (C3). This entails that the speaker does not know which book(s) Pedro bought. Crucially, the singleton competitors can be false while the possible assertions are true—that is, none of the singleton competitors expresses the same proposition as any of the possible assertions (even if, e.g., C1 entails A1, since A1 does not entail C1).12, 13 To see the effects that the new semantics for algún proposed in Section 3.2 has, consider (37). (37) combines the paucal semantics for algún with AO&MB’s anti-singleton requirement. The meaning expressed by (32) is now (38): (37)
[[algún (P)]] = λS: anti-singl(f).∃z (f(Q))(z) & Q⊏P & ¬∀y (Q(y)→Q(z⊔y)) & S(z)
12
AO&MB (2010) propose a slightly different analysis for number ignorance implicatures, which I don’t discuss here. 13 AO&MB (2010) develop slightly different accounts for cases where algún is embedded under necessity modals vs. possibility modals. They extend their account to (superficially) unmodalized sentences by assuming a covert modal operator with a doxastic semantics.
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(38)
BS ∃z z∈f({b1, b2, b3, b1+b2, b1+b3, b2+b3, b1+b2+b3}) & bought (z)(Pedro)
Some of the possible assertions expressed by (38) are as follows: (39)
A1: BS ∃z z∈{b1, b2} & bought(z)(Pedro) A2: BS ∃z z∈{b1, b1+b2} & bought(z)(Pedro) A3: BS ∃z z∈{b2, b1+b2} & bought(z)(Pedro) A4: BS ∃z z∈{b3, b2+b3} & bought(z)(Pedro) A5: BS ∃z z∈{b1+b2, b1+b2+b3} & bought(z)(Pedro) A6: BS ∃z z∈{b1+b3, b1+b2+b3} & bought(z)(Pedro) A7: BS ∃z z∈{b2+b3, b1+b2+b3} & bought(z)(Pedro) A8: BS ∃z z∈{b1+b3, b1+b2, b2+b3} & bought(z)(Pedro)…
The hearer again asks why the speaker chose to assert (38), with an anti-singleton requirement, and then reasons that she did so because no singleton domain would have been conducive to truth. The singleton competitor assertions are in (40): (40)
C1: BS ∃z z∈{b1} & bought(z)(Pedro) C2: BS ∃z z∈{b2} & bought(z)(Pedro) C3: BS ∃z z∈{b3} & bought(z)(Pedro) C4: BS ∃z z∈{b1+b2} & bought(z)(Pedro) C5: BS ∃z z∈{b1+b3} & bought(z)(Pedro) C6: BS ∃z z∈{b2+b3} & bought(z)(Pedro) C7: BS ∃z z∈{b1+b2+b3} & bought(z)(Pedro)
The problem is that most of the competitor assertions in (40) cannot be false, since they are equivalent to at least one of the possible assertions in (39). For example, C1 is equivalent to A2. That’s because C1 entails A2 (since p entails p ∨ q), and A2 entails C1 (since C1 is true if the first disjunct in A2 is true, and the second disjunct in A2 entails the first disjunct). Likewise, C2 is equivalent to A3, C3 is equivalent to A4, C4 is equivalent to A5, C5 is equivalent to A6, and C6 is equivalent to A7. The only competitor assertion that can be false is C7—this correctly derives a not-many/all implicature, but no identity (or number) ignorance implicature is generated here. Thus, the proposal made in this paper regarding the number semantics of algún entails that AO&MB’s account of its ignorance implicatures cannot be maintained. AO&MB (2011) assume that the domain of algunos is formed of atoms and non-atoms. While I have argued here that the domain of this determiner is formed of non-atoms only, AO&MB demonstrate in their paper that the lack of
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implicatures with algunos follows in either case.14 For completeness, I now repeat that account here. The meaning for algunos that combines its greater paucal semantics and AO&MB’s anti-singleton requirement is in (41): (41)
[[algunos (P)]] = λS: anti-singl(f). ∃z (f(Q))(z) & Q⊏{x: R(x) & R⊏P & ∀v (R(v)→R(x⊔v))} & ¬∀y (Q(y)→Q(z⊔y))] & S(z)
(42)
Pedro se compró algunos libros en Pedro SE bought ALGUNOS books in ‘Pedro bought himself several books at the fair.’
(43)
BS ∃z z∈f({b1+b2+b3, b1+b2+b4, b1+b2+b5, b2+b3+b4, b2+b3+b5,…, b1+b2+b4+b5,…, b1+b2+b3+b4+b5}) & bought(z)(Pedro)
(44)
A1: BS ∃z z∈{b1+b2+b3, b1+b2+b4} & bought(z)(Pedro) A2: BS ∃z z∈{b1+b2+b3, b1+b2+b3+b5} & bought(z)(Pedro) A3: BS ∃z z∈{b2+b3+b4+b5, b1+b2+b3+b4+b5} & bought(z)(Pedro) A4: BS ∃z z∈{b1+b2+b3+b5, b1+b2+b3+b4+b5} & bought(z)(Pedro)…
la the
feria. fair
The hearer will again conclude that all of the singleton competitors to the possible assertions in (44), some of which are in (45), are false: (45)
C1: BS ∃z z∈{b1+b2+b3} & bought(z)(Pedro) C2: BS ∃z z∈{b1+b2+b4} & bought(z)(Pedro) C3: BS ∃z z∈{b1+b2+b5} & bought(z)(Pedro) C4: BS ∃z z∈{b2+b3+b4} & bought(z)(Pedro) C5: BS ∃z z∈{b2+b3+b4+b5} & bought(z)(Pedro) C6: BS ∃z z∈{b1+b2+b3+b4+b5} & bought(z)(Pedro)…
It is not possible for C1-C5 in (45) to be false, since they are equivalent to at least one of the possible assertions in (44)—this is reminiscent of the problem raised by paucal algún above, except that here it is not a problem, since algunos does not trigger ignorance implicatures (it is appropriate to ask which (or how many) books Pedro bought at the fair after a speaker utters (42)).
14
Though the latter makes wrong predictions for sentences with collective predicates, such as form a circle, since it predicts such sentences to generate an ignorance implicature about groups, as AO&MB (2011: 231-3) show.
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7 Conclusion In this paper I have argued that paucity occurs in the determiner domain. I have provided an analysis that transparently relates the paucal semantics of the Spanish indefinites algún and algunos to their form. I argued that alg- contributes Harbour’s (2014) [−additive] to both of them, and that -salgunos contributes his [+additive]. I also argued that plural morphology in regular nouns is interpreted as plural, and briefly discussed some of the issues that this raises. Finally, I showed that AO&MB’s account of the ignorance implicatures of algún cannot be maintained under the new paucal semantics argued for here for this indefinite. References Alonso-Ovalle, Luis and Paula Menéndez-Benito. 2010. Modal Indefinites. Natural Language Semantics 18, 1-31. doi: 10.1007/s11050-009-9048-4. Alonso-Ovalle, Luis and Paula Menéndez-Benito. 2011. Domain Restrictions, Modal Implicatures and Plurality: Spanish algunos. Journal of Semantics 28, 211-240. doi: 10.1093/jos/ffq016. Bennett, Michael. 1974. Some Extensions of a Montague Fragment of English. Ph.D. dissertation, UCLA, Los Angeles, California. Chierchia, Gennaro. 1998. Plurality of Mass Nouns and the Notion of ‘Semantic Parameter’. In Susan Rothstein (ed.), Events and Grammar, 53-103. Dordrecht: Kluwer Academic Publishers. Corbett, Greville. 2000. Number. Cambridge, UK: Cambridge University Press. Farkas, Donka and Henriëtte de Swart. 2010. The Semantics and Pragmatics of Plurals. Semantics and Pragmatics 3(6). 1–54. doi:10.3765/sp.3.6. Gutiérrez-Rexach, Javier. 2001. The Semantics of Spanish Plural Existential Determiners and the Dynamics of Judgment Types. Probus 13(1). 113-154. doi: 10.1515/prbs.13.1.113. Harbour, Daniel. 2014. Paucity, Abundance and the Theory of Number, Language 90, 158-229. doi: 10.1353/lan.2014.0003. Hoeksema, Jack. 1983. Plurality and Conjunction. In Alice G.B. ter Meulen (ed.), Studies in Model-Theoretic Semantics, 63-83. Dordrecht: Foris. Hutchisson, Don. 1986. Sursurunga Pronouns and the Special Uses of Quadral Number. In Ursula Wiesemann (ed.), Pronominal Systems, 217–55. Tübingen: Gunter Narr. Kratzer, Angelika and Junko Shimoyama. 2002. Indeterminate Pronouns: the View from Japanese. In Yukio Otsu (ed.), 3rd Tokyo Conference on Psycholinguistics, 1-25. Hituzi Syobo: Tokyo. Krifka, Manfred. 1989. Nominal Reference, Temporal Constitution and Quantification in Event Semantics. In Renate Bartsch, Johan van Benthem &
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Peter van Emde Boas (eds.), Semantics and Contextual Expression, Dordrecht: Foris. Krifka, Manfred. 1992. Thematic Relations as Links between Nominal Reference and Temporal Constitution. In Ivan Sag and Anna Szabolcsi (eds.), Lexical Matters, 29-53. Stanford, CA: CSLI Publications. Lasersohn, Peter. 1988. A semantics for Groups and Events, PhD dissertation, Ohio State University, Columbus, Ohio. Lasersohn, Peter. 2011. Mass Nouns and Plurals. In Klaus von Heusinger, Claudia Maienborn and Paul Portner (eds.), Semantics: An International Handbook of Natural Language Meaning, vol. 2, 1131-1153. Berlin: De Gruyter. Link, Godehard. 1983. The Logical Analysis of Plural and Mass Terms: a LatticeTheoretical Approach. In Rainer Bäuerle, Christoph Schwarze & Arnim von Stechow (eds.), Meaning, Use and Interpretation of Language, 302-323. Berlin: de Gruyter. López Palma, Helena. 2007. Plural Indefinite Descriptions with unos and the Interpretation of Number. Probus 19(2). 235-266. doi: 10.1515/PROBUS.2007.008. Martí, Luisa. 2007. Returning Indefinites to Normalcy: an Experimental Study on the Scope of Spanish algunos. Journal of Semantics 24(1). 1-25. doi: 10.1093/jos/ffl010. Martí, Luisa. 2008. The Semantics of Plural Indefinites in Spanish and Portuguese. Natural Language Semantics 16(1). 1-37. doi: 10.1007/s11050007-9023-x. Sauerland, Uli. 2003. A New Semantics for Number. In Rob Young & Yuping Zhou (eds.), Semantics and Linguistic Theory (SALT), 13, 258–275. Ithaca, N.Y: Cornell University CLC-Publications. Sauerland, Uli, Jan Anderssen and Kazuko Yatsushiro. 2005. The Plural is Semantically Unmarked. In Stefan Kepser and Marga Reis (eds.), Linguistic Evidence. Empirical, Theoretical and Computational Perspectives, 409–30. Berlin: de Gruyter. Berlin. Schwarzschild, Roger. 1996. Pluralities. Dordrecht: Kluwer Academic Publishers. Spector, Benjamin. 2007. Aspects of the Pragmatics of Plural Morphology: on Higher-Order Implicatures. In Uli Sauerland & Penka Stateva (eds.), Presuppositions and Implicatures in Compositional Semantics, 243–281. Hampshire, UK: Palgrave/MacMillan. Zamparelli, Roberto. 2007. On Singular Existential Quantifiers in Italian. In Ileana Comorovski and Klaus von Heusinger (eds.), Existence: Syntax and Semantics, 293-328. Dordrecht: Springer.
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Luisa Martí Mile End Road Queen Mary, University of London London, UK E1 4NS
[email protected]
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